3^(n+1)-3^(n-2)

Need help simplifying this please.

because multiplication of powers results in adding exponents, one can reduce this to

3^n*3^1 - 3^n*3^-2

3^n * (3-1/9)=3^n (2 8/9)

still don't really quite understand. could you explain your process a bit more?

Mara -- why are you butting in to richard's question?

To simplify the expression 3^(n+1) - 3^(n-2), we can use the properties of exponents. Let's break it down step by step.

Step 1: Expand the exponents.
Using the property a^(m + n) = a^m * a^n, we can rewrite the expression as follows:
3^n * 3^1 - 3^n * 3^(-2)

Step 2: Simplify the exponents.
1. 3^1 is equal to 3, since any number raised to the power of 1 is itself.
2. 3^(-2) is equal to 1/3^2 = 1/9, since any number raised to the power of -2 is equal to the reciprocal of that number raised to the power of 2.

Substituting the simplified exponents into the expression, we get:
3^n * 3 - 3^n * 1/9

Step 3: Combine like terms.
Since both terms have the same base, 3^n, we can factor it out:
3^n * (3 - 1/9)

Step 4: Simplify the expression further.
1. 3 - 1/9 = (27/9) - (1/9) = 26/9
2. Multiply 3^n by (26/9):
3^n * (26/9) = (26/9) * 3^n

Therefore, the simplified expression is (26/9) * 3^n.